Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
43501	Find the Asymptotes	f(x)=12/(1+2(0.9)^x)	$f (x) = \frac{12}{1 + 2 {(0.9)}^{x}}$
43502	Find the Asymptotes	f(x)=(5x)/(x-5)	$f (x) = \frac{5 x}{x - 5}$
43503	Find the Asymptotes	f(x)=-7/(x+1)	$f (x) = \frac{- 7}{x + 1}$
43504	Find the Asymptotes	f(x)=(5x-1)/(12x^2+9)	$f (x) = \frac{5 x - 1}{12 x^{2} + 9}$
43505	Find the Asymptotes	f(x)=x/(x^2-36)	$f (x) = \frac{x}{x^{2} - 36}$
43506	Find the Asymptotes	f(x)=(x^2)/(x-7)	$f (x) = \frac{x^{2}}{x - 7}$
43507	Find the Asymptotes	f(x)=(x^2)/(x^2-100)	$f (x) = \frac{x^{2}}{x^{2} - 100}$
43508	Split Using Partial Fraction Decomposition	(15x^2-11x-5)/(x(x+1)(2x-5))	$\frac{15 x^{2} - 11 x - 5}{x (x + 1) (2 x - 5)}$
43509	Split Using Partial Fraction Decomposition	(5x^3+32x-4)/((x^2+6)^2)	$\frac{5 x^{3} + 32 x - 4}{{(x^{2} + 6)}^{2}}$
43510	Split Using Partial Fraction Decomposition	(4x+9)/((x+9)(9x-1))	$\frac{4 x + 9}{(x + 9) (9 x - 1)}$
43511	Split Using Partial Fraction Decomposition	(3x-66)/((x-4)^2(x+5))	$\frac{3 x - 66}{{(x - 4)}^{2} (x + 5)}$
43512	Split Using Partial Fraction Decomposition	1/(x(2x+5)(3x^2+1))	$\frac{1}{x (2 x + 5) (3 x^{2} + 1)}$
43513	Split Using Partial Fraction Decomposition	( square root of 3-x)/((x+6)(x^2+1))	$\frac{\sqrt{3 - x}}{(x + 6) (x^{2} + 1)}$
43514	Solve by Substitution	x-2y=3x-y^2=0	$x - 2 y = 3 x - y^{2} = 0$
43515	Solve by Substitution	x+y=5y=x^2-1	$x + y = 5 y = x^{2} - 1$
43516	Solve by Substitution	x-y+2z=1-x-2y-z=3-3x-3y-4z=5	$x - y + 2 z = 1 - x - 2 y - z = 3 - 3 x - 3 y - 4 z = 5$
43517	Solve by Substitution	xy=12x^2+y^2=40	$x y = 12 x^{2} + y^{2} = 40$
43518	Solve by Substitution	x+2y=44x+8y=16	$x + 2 y = 44 x + 8 y = 16$
43519	Solve by Substitution	x^2+y^2=49y=x-7	$x^{2} + y^{2} = 49 y = x - 7$
43520	Solve by Substitution	x^2+y^2-x-y-12=0x+y+4=0	$x^{2} + y^{2} - x - y - 12 = 0 x + y + 4 = 0$
43521	Solve by Substitution	16x^2+4y^2=64 , y=x^2-4	$16 x^{2} + 4 y^{2} = 64$ , $y = x^{2} - 4$
43522	Solve by Substitution	2x+4y=-3.89x-5y=1.3	$2 x + 4 y = - 3.89 x - 5 y = 1.3$
43523	Solve by Substitution	2x+6y=-2812x+3y=63	$2 x + 6 y = - 2812 x + 3 y = 63$
43524	Solve by Substitution	2x-3y-9z=-5x+3z=2-3x+y-4z=-3	$2 x - 3 y - 9 z = - 5 x + 3 z = 2 - 3 x + y - 4 z = - 3$
43525	Solve by Substitution	3x^2+2y^2=2x-y=-1	$3 x^{2} + 2 y^{2} = 2 x - y = - 1$
43526	Solve by Substitution	6x-3y-8=0x+4y-8=0	$6 x - 3 y - 8 = 0 x + 4 y - 8 = 0$
43527	Solve by Substitution	6x-8y=-0.63x+2y=0.9	$6 x - 8 y = - 0.63 x + 2 y = 0.9$
43528	Solve by Substitution	x^2+xy=30x^2+2xy=-4	$x^{2} + x y = 30 x^{2} + 2 x y = - 4$
43529	Split Using Partial Fraction Decomposition	(7x+3)/(x^3-2x^2-3x)	$\frac{7 x + 3}{x^{3} - 2 x^{2} - 3 x}$
43530	Split Using Partial Fraction Decomposition	x/(x^2+6x-7)	$\frac{x}{x^{2} + 6 x - 7}$
43531	Split Using Partial Fraction Decomposition	x/(x^2-5x-36)	$\frac{x}{x^{2} - 5 x - 36}$
43532	Split Using Partial Fraction Decomposition	x/(x^2-7x-18)	$\frac{x}{x^{2} - 7 x - 18}$
43533	Split Using Partial Fraction Decomposition	x/(x^2-2x-35)	$\frac{x}{x^{2} - 2 x - 35}$
43534	Split Using Partial Fraction Decomposition	(x-12)/(x^2-4x)	$\frac{x - 12}{x^{2} - 4 x}$
43535	Split Using Partial Fraction Decomposition	(x-6)/((x-3)(x-4))	$\frac{x - 6}{(x - 3) (x - 4)}$
43536	Split Using Partial Fraction Decomposition	(x^2+x-182)/((x+5)^2(x-4))	$\frac{x^{2} + x - 182}{{(x + 5)}^{2} (x - 4)}$
43537	Find the Roots/Zeros Using the Rational Roots Test	f(x)=2x^4-5x^3-20x^2+115x-52	$f (x) = 2 x^{4} - 5 x^{3} - 20 x^{2} + 115 x - 52$
43538	Solve the Triangle	tri{8}{}{}{}{6}{}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 8 \\ c = \\ a = & 6 \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$
43539	Find the Roots/Zeros Using the Rational Roots Test	f(x)=2x^3-4x^2-38x+76	$f (x) = 2 x^{3} - 4 x^{2} - 38 x + 76$
43540	Solve by Substitution	y^2=x^2-64-3y=x+8	$y^{2} = x^{2} - 64 - 3 y = x + 8$
43541	Solve the Triangle	tri{31.4}{}{38.5}{}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 31.4 \\ c = & 38.5 \\ a = \end{matrix} & \begin{matrix} A = \\ B = \\ C = & 90 \end{matrix} \end{matrix}$
43542	Solve the Triangle	tri{10}{}{10}{}{8}{}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 10 \\ c = & 10 \\ a = & 8 \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$
43543	Identify the Conic	x^2-y^2-6x-12y+9=0	$x^{2} - y^{2} - 6 x - 12 y + 9 = 0$
43544	Identify the Conic	9x^2+16y^2+54x-32y-47=0	$9 x^{2} + 16 y^{2} + 54 x - 32 y - 47 = 0$
43545	Identify the Conic	4x^2+4y^2+40x+16y+40=0	$4 x^{2} + 4 y^{2} + 40 x + 16 y + 40 = 0$
43546	Identify the Conic	3x^2+12y^2-9x+12y-9=0	$3 x^{2} + 12 y^{2} - 9 x + 12 y - 9 = 0$
43547	Identify the Conic	(y-2)^2=12(x+7)	${(y - 2)}^{2} = 12 (x + 7)$
43548	Convert to Degrees, Minutes, and Seconds	118.32 degrees	$118.32 °$
43549	Find the Vertex	x^2-6x+4	$x^{2} - 6 x + 4$
43550	Find the Derivative - d/d@VAR	f(x)=(5x^4+3x^2-x)/(x^3)	$f (x) = \frac{5 x^{4} + 3 x^{2} - x}{x^{3}}$
43551	Find the Derivative - d/d@VAR	f(x)=4-3x^2	$f (x) = 4 - 3 x^{2}$
43552	Find the Union of the Sets	tri{}{}{}{}{}{}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$
43553	Describe the Transformation	y=-7sec(x)	$y = - 7 \sec (x)$
43554	Describe the Transformation	y=csc(x)-9	$y = \csc (x) - 9$
43555	Solve for z	natural log of z^3-2 natural log of z=e	$\ln (z^{3}) - 2 \ln (z) = e$
43556	Solve for z	3 = square root of 5z-7+10	$3 = \sqrt{5 z - 7} + 10$
43557	Solve for z	(1/5000)^(-2z)*5000^(-2z+2)=5000	${(\frac{1}{5000})}^{- 2 z} \cdot 5000^{- 2 z + 2} = 5000$
43558	Solve for z	1/x+1/y=1/z	$\frac{1}{x} + \frac{1}{y} = \frac{1}{z}$
43559	Solve for y	y=arctan(tan((2pi)/3))	$y = \arctan (\tan (\frac{2 π}{3}))$
43560	Solve for z	z^4=-625	$z^{4} = - 625$
43561	Solve for z	z=1/2+( square root of 3)/2i	$z = \frac{1}{2} + \frac{\sqrt{3}}{2} i$
43562	Solve for z	z=6.2+37i	$z = 6.2 + 37 i$
43563	Find the Circle Using the Diameter End Points	(-3,5) , (1,9)	$(- 3, 5) (1, 9)$
43564	Solve for w	w(27-w)=120	$w (27 - w) = 120$
43565	Solve for v	square root of v = square root of 15-2v	$\sqrt{v} = \sqrt{15 - 2 v}$
43566	Solve for v	v=7i-7j	$v = 7 i - 7 j$
43567	Solve for t	i=prt	$i = p r t$
43568	Solve for t	75=-15cos((2pi)/15t)+65	$75 = - 15 \cos (\frac{2 π}{15} t) + 65$
43569	Solve for t	750=52sin((2pi)/365t)+728	$750 = 52 \sin (\frac{2 π}{365} t) + 728$
43570	Solve for t	5.2=1.5cos((2pi)/365t)+4.3	$5.2 = 1.5 \cos (\frac{2 π}{365} t) + 4.3$
43571	Solve for t	5000=25000(1-0.3)^t	$5000 = 25000 {(1 - 0.3)}^{t}$
43572	Solve for t	cos(t)=1	$\cos (t) = 1$
43573	Solve for t	9000=12000*2^(-t/15)	$9000 = 12000 \cdot 2^{- \frac{t}{15}}$
43574	Solve for t	x=4t-1	$x = 4 t - 1$
43575	Solve for t	x=1/2t	$x = \frac{1}{2} t$
43576	Solve for t	t=-216 degrees	$t = - 216 °$
43577	Solve for y	square root of 7y^2+15y-2y=5+y	$\sqrt{7 y^{2} + 15 y} - 2 y = 5 + y$
43578	Solve for y	(x+10)^2=4(26/125)(y+210)	${(x + 10)}^{2} = 4 (\frac{26}{125}) (y + 210)$
43579	Solve for y	natural log of 3y+5- natural log of y-1 = natural log of -4y+10	$\ln (3 y + 5) - \ln (y - 1) = \ln (- 4 y + 10)$
43580	Solve for y	log of y=4	$\log (y) = 4$
43581	Solve for y	2/5(y+10)=8	$\frac{2}{5} (y + 10) = 8$
43582	Solve for y	3y+2 = square root of y^2+10y+7	$3 y + 2 = \sqrt{y^{2} + 10 y + 7}$
43583	Solve for y	-1.1y-16.9>=4.1(1-y)	$- 1.1 y - 16.9 \geq 4.1 (1 - y)$
43584	Solve for y	y=cos(arcsin(1/6))	$y = \cos (\arcsin (\frac{1}{6}))$
43585	Solve for y	y^2=5^2-4^2	$y^{2} = 5^{2} - 4^{2}$
43586	Solve for y	y=601(1.05)^18	$y = 601 {(1.05)}^{18}$
43587	Solve for h	A=1/2(b_1+b_2)h	$A = \frac{1}{2} (b_{1} + b_{2}) h$
43588	Solve for b	b+4 = square root of 6b+15	$b + 4 = \sqrt{6 b + 15}$
43589	Solve for n	-1 = square root of n-5	$- 1 = \sqrt{n} - 5$
43590	Solve for n	square root of n = square root of 2n-6	$\sqrt{n} = \sqrt{2 n - 6}$
43591	Solve for n	(2n-3)/2=3/4	$\frac{2 n - 3}{2} = \frac{3}{4}$
43592	Solve for n	square root of 2n-88 = square root of n/6	$\sqrt{2 n - 88} = \sqrt{\frac{n}{6}}$
43593	Solve for m	K=1/2mv^2	$K = \frac{1}{2} m v^{2}$
43594	Solve for m	m-1 = square root of 5m-5	$m - 1 = \sqrt{5 m - 5}$
43595	Solve for k	1000e^(k(1))=1500	$1000 e^{k (1)} = 1500$
43596	Solve for k	square root of 1-k- square root of 3k+1=-2	$\sqrt{1 - k} - \sqrt{3 k + 1} = - 2$
43597	Solve for k	square root of 2k+1=-21	$\sqrt{2 k + 1} = - 21$
43598	Solve for k	natural log of 1/2=19k	$\ln (\frac{1}{2}) = 19 k$
43599	Solve for l	A=lw	$A = l w$
43600	Solve for m	10+ square root of 10m-1=13	$10 + \sqrt{10 m - 1} = 13$